Refining the Highest-Die roll mechanic

[Don Lag]

When I began thinking of a funky new way to create probability distributions for my game, it didn't take long to stumble upon the idea in which you roll a certain amount of dice against another amount of dice and then just compare the highest result on each. The probability curve was interesting enough as you started adding more dice to a given roll, and the probability for winning on a challenged roll was equally simple. Add to that the fact that no matter how many dice you roll you always cover the same range of numbers (it just gets very improbable that you roll a 1). I loved this mechanic.

I started looking on the web and found others that used the same mechanic (although with their own modifications). First it was the DP9 games with their Silhouette, and then Ron's Sorceror among others.

It seems to me that this has become (or is becoming) a rather popular mechanic; noticeably because it requires small-numbered math on the character sheets, it keeps a uniform range of results (something that doesn't happen when you add modifiers to a single die), is very quick to resolve (you just pick the highest!).

I'm now in the process of refining my mechanic, which basically means I'm deciding how to handle special cases and how to represent certain phenomena in the mechanic. I'd love to hear opinions, observations, etc. regarding this mechanic. I'm definately not trying to rip off anyone's solutions, but rather listen to their reasons for why they've prefered one solution to another. I guess this post is directed mainly to game designers who have chosen this mechanic, or considered it at least, but general player's experience is welcome also.

As of now, my mechanic is just vanilla: you roll N dice pick the highest. Roll M oppossing dice and choose the highest. Compare both results to tell which way the results lean. I'll suppose this defines the "type" of mechanic I'm talking about, and that most actual implementations of this type include modifications or additions to this base. My main goal is keeping it simple, fast and fun,  while retaining as much simulationist richness as possible.

1) Degrees of success
My first try was counting how many dice of the roll were greater than the highest of the opposing roll (I think Sorceror uses this, correct me if I'm wrong). So a roll of  7, 6, 4 gets to successes over a 5, 3, 3. Downside: it added more complexity than I think I wanted. I've only tested it once, and it seemed like an obstacle in that ocassion.

But I guess I'll still end up using it in some way or another, the really good part is it translates cleanly into damage resolution for combat.

Another idea I just can't get convinced of is subtracting results. A 12, 8, 4 against a 7, 4, 3 yields a success of 5 (12-7). I find this akward in that you start caring about numbers which are on another scale (dice-count scale vs dice-sides scale). All character scores in my game are on the dice-count scale (numbers between 1 and 5 usually), while the dice used are d20s.

As a third idea, which I found sorta cute, was that you re-rolled the opposing roll as many times as necessary until you beat the action roll. The number of times needed to beat the roll would count as the degree of success. Downside: you could potentially take a really long time re-rolling stuff. A modification to this would be subtracting a die on each re-roll (limiting the amount of re-rolls), but it's seems to be just too much fuss.

2) Bonuses and Penalties

I guess most bonuses wil be in the form of adding one or more dice. Using modifiers that are to be added to the die requieres math on the dice-sides scale, and shifts the results range, leaving certain results out of range.

If you add dice for bonus, the mst normal thing to do seems to be subtract for penalties. I'm still not sure what to do with penalizing a 1-die roll though... or a roll with -1 dice?

Another solution for penalizing is that instead of choosing the highest die, you choose the next-highest die, and so on. So if you have a penalization of -2 you choose the third highest die as your result. Downside: it turns out to be somewhat slow and confusing, doesn't solve the penalizd 1-die roll, and penalizes the roll a little "too much" (a lot more than just subtracting dice).

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There are a lot more aspects of this mechanic that I think are worth discussion (for example, I've found that there are very elegant ways to stem simultaneous and chained action resolution), but I'd like to see if there is any interest first and what observations might arise from the basic problems exposed above.

PS: I'm not calling for detailed descriptions of other's systems, and I wouldn't consider exposing them as appropriate unless the author's permission is given.

[Jared A. Sorensen]

As a third idea, which I found sorta cute, was that you re-rolled the opposing roll as many times as necessary until you beat the action roll. The number of times needed to beat the roll would count as the degree of success.

Kinda spinning off that idea, you get to re-roll the highest die by sacrificing a Level of Effect -- so instead of success, you get a middling success. Instead of a middling succes, you get a minor failure...etc, etc.

[lumpley]

For penalty dice you can subtract dice down to one, then switch to the lowest die.  Like this:

4 - roll 4d, take the highest
3 - roll 3d, take the highest
2 - roll 2d, take the higher
1 - roll 1d, take it
0 - roll 2d, take the lower
-1 - roll 3d, take the lowest

etc.

Personally, I always preferred roll n dice and take the second highest, for the downturn at the right side of the curve, which I think is pretty.  You get a broader distribution at higher numbers of dice; if you're rolling 6d10 and taking the highest, you get a 9 or a 10 practically every roll.  Taking the second highest shakes that up.

Or, for d6s, roll nd6 and add the highest two.

5d20 take the middle one gives you as nice a bell curve as you could want.  I just can't bring myself to ask anybody to roll 5d20 and take the middle one, in play.

It's also fun, especially with the broader curves that taking the second highest die gives you, to throw in dice of different sizes.  If you're rolling mostly d6s, for instance, a d4 is about a half-bonus, and a d8 is not quite a double-bonus.  In some stillborn fantasy game I was making a hundred years ago, that's how I differentiated the weapons.  A dagger added a d4 to your roll, a sword a d6, a greatsword a d8...

-lumpley Vincent

[Don Lag]

Great idea Jared... you've already got me thinking in at least 3 ways in which this can be implemented (saving dice for re-rolling, getting re-rolling dice from "tools", etc)...

but they're kinda of comlpicated, I think it's best to stick to a simpler implementation.

Here's a shot:

You've got 6 ranks of results:
Great success
Normal success
marginal success
marginal failure
normal failure
great failure

You roll your straight roll, if you win, you get a Normal Success. You can choose to re-roll, if your re-roll also beats the opposing roll you get a Great Success, if you fail, you get a Marginal Success.

If you fail the straight roll, you get a Normal Failure, if you choose to re-roll and win you get a Marginal Failure, if you lose you get a Great Failure.

Actually, I think this exactly what you were suggesting, just more exhaustively elaborated :smile:

I like it, except that it adds an extra roll (kinda reminds of Palladium's roll w/punch). I think limiting the use of this would be positive. For example, if you have 4 dice for a given action, you can choose to save 1 die for re-rolling, using only 3 for the straight roll. This also makes having more dice a more versatile advantage (although I'm not sure it would be wise to allow for more than 1 re-roll, it'd just slow things down I think).

Finally, even with this modification, I see a problem where characters with 1 die can't get Great Successes. Maybe a result of 20 on the straight roll starts off as a Great Success (that can be re-rolled into a Exceptional Success or something, or down to a Normal Success, if you have a saved die).

Thanks a lot Jared, this was just too useful, you totally got me out of the blockage I had fallen into :smile: :smile:

Lumpley:

I had thought of that idea too. The problem is that the punishment recieved by taking a lower dice from a roll isn't the same as subtracting a die altogether (limit example: rolling 20 with 1 die=1/20, rolling 20 by taking the lowest of two=1/400). This isn't necessarily bad, you could argue that once you're in "negatives" it just gets worse and worse... but then you come to the point that really makes it uncomfortable: it's a pain to choose anything from the third highest die or lower.

But I still don't know, I mean, I don't think rolling in "negatives" would be to common anyway so maybe it's good enough. I'll try to test it though before I make a final decision.

[Paul Czege]

Hey Vincent,

Personally, I always preferred roll n dice and take the second highest, for the downturn at the right side of the curve, which I think is pretty.

I like this a lot. It would be perfectly thematically appropriate for a somewhat melancholy game setting, where "you're never as good as you think you are." It always takes you longer to get where you're driving than you think it will. You always have to make a trip to the hardware store in the middle of the project, because you didn't anticipate everything. A nice metagame mechanic would be some kind of point pool you spend to use the highest die from the roll, rather than the second highest.

Paul

[Don Lag]

Yeah, taking the second die does give a somewhat frustrating mechanic :smile:

And just to attend a comment Vincent made, I don't think this system is very useful for small sided dice, the high number probability spikes too quickly for low dice pools (using 4d20 you already have a little more than 50% chance of rolling >=17).

That's why I'd just LOVE to use d30s!!! It would give a much better resolution at higher dice pools.

[kwill]

if you're looking for another knob to turn in setting/determining difficulty, how about dice type?

if you're currently rolling pools of Md versus Nd, consider MdX versus NdY, where of course M & N may be equal, or X & Y may be equal

while someone rolling d6's may be outclassed by someone rolling d12's (for example), there's always a chance he'll succeed (or, more to the point, that the other guy will mess up)

I'm not sure if the curves do funny things like crossing over at certain points, though (I thought my idea for |dX - dY| was great until I had a look at it in excel, some curves crossed each other twice!)

[Ron Edwards]

Hey,

I'm not sure where to go with this, except to say that a huge amount of debate about this mechanic is incorporated both into Sorcerer's design and to any number of threads both here and on GO.

One of the older comments is found http://www.sorcerer-rpg.com/brochure.php/list7.html">here in the Sorcerer mailing list archives. Another is http://www.indie-rpgs.com/forum/viewtopic.php?topic=540&forum=7&2">here on the Sorcerer forum.

Obviously, no one "owns" a mechanic, and I look forward to more discussion and development for other games.

Best,
Ron

P.S. Oh, and for the record, Sorcerer's earliest commercially available form predates Dream Pod 9, Ironclaw, and Deadlands (the other read-high-die systems).

[ This Message was edited by: Ron Edwards on 2001-11-16 10:18 ]

[Matt Machell]

Don, a brief idea I had when playing with IMP (which uses a similar mechanic), degree of success is equal to the number of dice which roll the same as your highest. Makes getting higher degrees of success harder but still possible.

Just a thought.


Matt

[lumpley]

Melancholy?  Frustrating?  

Weird.  I just kind of like playing in both halves of the bell curve.

But no, for small dice, adding the two highest is how I'd go every time.  I forget the numbers precisely (it's been some years) but it wasn't until like 7d6 that you stopped noticing more dice.

Oh, but I was just using that number (highest die, second highest die, sum of two highest dice, whichever) for the degree of success.  If you have some other way to determine degree of success, like Sorcerer's, you don't care about the curve of the raw dice.  You care about some other curve: my highest vs yours, for instance.

-lumpley Vincent

[Don Lag]

Kwill, in fact the version 1.0 of Oscura had you choosing any type of die you wanted: if you had 3 dice for horseback riding, for example, you could choose to roll 3d4, 3d10, 3d20 or whatever. The GM was supposed to be able to limit the dice type under certain circumstances (for example, if your hands were tied together you might be allowed only up to d10s). The thing you also had a sort of "stress" number associated with every score (or a few general stress numbers, whatever). If your roll exceeded the stress number (for example, if you were a mediocre horseback rider, you'd have a stres number of 10 or 8 maybe) you'd start to lose dice from your "pool" (acting above your stress number indicated that you were working "hard" for something to happen, ergo you'd start to wear out). It had a few interesting points in it, but it proved just too complicated. I might go back to allowing different types of dice, but for the moment I really like the idea of using a single type of die, it's less hassle.

Ron, I'll check out the threads you mention,thanks for pointing to them.

Vincent, actually choosing the median die of 3 doesn't yield a bell curve (not in the sense that a bell curve is a Guassian bell curve), but rather a parabola. Choosing the second-highest die would also yield a strange bell-like curve, but not the normal-distribution-Gaussian-bell-curve that is oh so useful in much of statistics and probabilites (just in case someone really cares about the technical stuff).

[lumpley]

Don Lag,

Naturally.  At 5 dice take the middle one you start to get flattening at the two extremes, like a bell curve's, but it's still a curve made of line segments not curves and it doesn't go out to wherever.

If, say, you start with 5d20 and take the third highest (the middle one), then add d20s and keep taking the third highest, you start with a symmetric bellish curve and as you add dice the hump shifts rightward in a way that I found pleasing.  As you become more skilled, it says, your normal performance gets better and better, but your performance still always falls into the absolute range of worst-possible to best-possible.

I liked skewing the curve better than shifting the curve, as you'd get if you just added your skill number to the 5d20-median roll.  I don't really remember why.

At that stage, my game designs were all about making d6s act in bell-curvish ways.

Oh, and this goes back a couple posts: as far as negative dice go, that's exactly what I'd argue.

-lumpley Vincent


[ This Message was edited by: lumpley on 2001-11-17 14:53 ]

[Don Lag]

Actually I reviewed the function I got last time I looked at the median roll and realized that you're right. I originally ran the tests for only 3 dice so the flattening wasn't evident, but at 7+ dice it really starts to show (it's still very mild at 5 dice). The distribution is actually a polynomial curve of an order one less than the number of dice (which explains no flattening at 3 dice, but some happening beyond that). Actually an approximate bell is good enough for most purposes.

What I'd see as the real downside though, is that as you increase the dice, you get a more "normal" behaviuor. This is, you have less chance of getting a 20 on rolling 7 dice than 3 (you alsom get less chance of rolling very low too). So what happens is that the more dice you have, the more stuck in the middle numbers (near 10) you get. So IMHO, just increasing dice numbers doesn't work for modelling advancement of expertise. (Reducing dice neither, since it just makes a more disperse distribution).

Ok, now I just modified it to see what happens on rolling N dice and always choosing the 3rd highest die for example, or Lth highest die in general.

Adding dice under this mechanic, as Vincent already pointed out, you get a bellish curve that starts skewing over to the higher numbers. I think this is more interesting. As long as you keep the die to look at fixed (i.e. always look at the second-highest die), when you add more dice to the roll you get higher probabilities for high results and start lowering it for smaller results.

Pretty nice, I'll send anyone interested the Excel sheet I worked with.

Thre's a second aspect of this result that I think merits attention. When rolling a varying number of dice, but always choosing the second highest (for example), then what happens is that you get higher results on average (for 6 dice you'd mostly get 17s), but beyond that average probabilities decrease. This is great when a result has a static meaning. For example, when you compare the roll to a table or a static number whose value is linear (protection class 16 is twice as good as protection class :cool:. But when you compare two rolls against each other, I think that this phenomenon appears by itself. So in my case, where you roll against an opposing roll, you wouldn't really gain much. I haven't looked at it very close yet, but I think tht's where it's going.

I'd be happy to comment further on this, especially considering that I've wrote a somewhat confusing post :smile:

Thanks for the comments Vincent.